论文标题
不是两部分图的两部分图
A Bipartite Graph That Is Not the $γ$-Graph of a Bipartite Graph
论文作者
论文摘要
对于图$ g =（v，e）$，$ g $的$γ$ - graph是其顶点集的图形，即最低主导集的集合，或$ g $的$γ$ - 集的$ g $，而两个$γ$ -SET在单个顶点和两个不同的顶点与$ g $相邻的情况相邻，则它们会相邻。 $γ$ - 图中的一个空旷的问题是，每个两部分图是某些两部分图的$γ$ - 图。我们通过证明$ k_ {2，3} $不是任何两部分图的$γ$ - 绘图来回答这个问题。
For a graph $G = (V, E)$, the $γ$-graph of $G$ is the graph whose vertex set is the collection of minimum dominating sets, or $γ$-sets of $G$, and two $γ$-sets are adjacent if they differ by a single vertex and the two different vertices are adjacent in $G$. An open question in $γ$-graphs is whether every bipartite graph is the $γ$-graph of some bipartite graph. We answer this question in the negative by demonstrating that $K_{2, 3}$ is not the $γ$-graph of any bipartite graph.
